6,869 research outputs found
Recurrent backpropagation and the dynamical approach to adaptive neural computation
Error backpropagation in feedforward neural network models is a popular learning algorithm that has its roots in nonlinear estimation and optimization. It is being used routinely to calculate error gradients in nonlinear systems with hundreds of thousands of parameters. However, the classical architecture for backpropagation has severe restrictions. The extension of backpropagation to networks with recurrent connections will be reviewed. It is now possible to efficiently compute the error gradients for networks that have temporal dynamics, which opens applications to a host of problems in systems identification and control
Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation
The control of nonlinear dynamical systems remains a major challenge for
autonomous agents. Current trends in reinforcement learning (RL) focus on
complex representations of dynamics and policies, which have yielded impressive
results in solving a variety of hard control tasks. However, this new
sophistication and extremely over-parameterized models have come with the cost
of an overall reduction in our ability to interpret the resulting policies. In
this paper, we take inspiration from the control community and apply the
principles of hybrid switching systems in order to break down complex dynamics
into simpler components. We exploit the rich representational power of
probabilistic graphical models and derive an expectation-maximization (EM)
algorithm for learning a sequence model to capture the temporal structure of
the data and automatically decompose nonlinear dynamics into stochastic
switching linear dynamical systems. Moreover, we show how this framework of
switching models enables extracting hierarchies of Markovian and
auto-regressive locally linear controllers from nonlinear experts in an
imitation learning scenario.Comment: 2nd Annual Conference on Learning for Dynamics and Contro
Complexity without chaos: Plasticity within random recurrent networks generates robust timing and motor control
It is widely accepted that the complex dynamics characteristic of recurrent
neural circuits contributes in a fundamental manner to brain function. Progress
has been slow in understanding and exploiting the computational power of
recurrent dynamics for two main reasons: nonlinear recurrent networks often
exhibit chaotic behavior and most known learning rules do not work in robust
fashion in recurrent networks. Here we address both these problems by
demonstrating how random recurrent networks (RRN) that initially exhibit
chaotic dynamics can be tuned through a supervised learning rule to generate
locally stable neural patterns of activity that are both complex and robust to
noise. The outcome is a novel neural network regime that exhibits both
transiently stable and chaotic trajectories. We further show that the recurrent
learning rule dramatically increases the ability of RRNs to generate complex
spatiotemporal motor patterns, and accounts for recent experimental data
showing a decrease in neural variability in response to stimulus onset
Differential Dynamic Programming for time-delayed systems
Trajectory optimization considers the problem of deciding how to control a
dynamical system to move along a trajectory which minimizes some cost function.
Differential Dynamic Programming (DDP) is an optimal control method which
utilizes a second-order approximation of the problem to find the control. It is
fast enough to allow real-time control and has been shown to work well for
trajectory optimization in robotic systems. Here we extend classic DDP to
systems with multiple time-delays in the state. Being able to find optimal
trajectories for time-delayed systems with DDP opens up the possibility to use
richer models for system identification and control, including recurrent neural
networks with multiple timesteps in the state. We demonstrate the algorithm on
a two-tank continuous stirred tank reactor. We also demonstrate the algorithm
on a recurrent neural network trained to model an inverted pendulum with
position information only.Comment: 7 pages, 6 figures, conference, Decision and Control (CDC), 2016 IEEE
55th Conference o
Recognizing recurrent neural networks (rRNN): Bayesian inference for recurrent neural networks
Recurrent neural networks (RNNs) are widely used in computational
neuroscience and machine learning applications. In an RNN, each neuron computes
its output as a nonlinear function of its integrated input. While the
importance of RNNs, especially as models of brain processing, is undisputed, it
is also widely acknowledged that the computations in standard RNN models may be
an over-simplification of what real neuronal networks compute. Here, we suggest
that the RNN approach may be made both neurobiologically more plausible and
computationally more powerful by its fusion with Bayesian inference techniques
for nonlinear dynamical systems. In this scheme, we use an RNN as a generative
model of dynamic input caused by the environment, e.g. of speech or kinematics.
Given this generative RNN model, we derive Bayesian update equations that can
decode its output. Critically, these updates define a 'recognizing RNN' (rRNN),
in which neurons compute and exchange prediction and prediction error messages.
The rRNN has several desirable features that a conventional RNN does not have,
for example, fast decoding of dynamic stimuli and robustness to initial
conditions and noise. Furthermore, it implements a predictive coding scheme for
dynamic inputs. We suggest that the Bayesian inversion of recurrent neural
networks may be useful both as a model of brain function and as a machine
learning tool. We illustrate the use of the rRNN by an application to the
online decoding (i.e. recognition) of human kinematics
Random Recurrent Neural Networks Dynamics
This paper is a review dealing with the study of large size random recurrent
neural networks. The connection weights are selected according to a probability
law and it is possible to predict the network dynamics at a macroscopic scale
using an averaging principle. After a first introductory section, the section 1
reviews the various models from the points of view of the single neuron
dynamics and of the global network dynamics. A summary of notations is
presented, which is quite helpful for the sequel. In section 2, mean-field
dynamics is developed.
The probability distribution characterizing global dynamics is computed. In
section 3, some applications of mean-field theory to the prediction of chaotic
regime for Analog Formal Random Recurrent Neural Networks (AFRRNN) are
displayed. The case of AFRRNN with an homogeneous population of neurons is
studied in section 4. Then, a two-population model is studied in section 5. The
occurrence of a cyclo-stationary chaos is displayed using the results of
\cite{Dauce01}. In section 6, an insight of the application of mean-field
theory to IF networks is given using the results of \cite{BrunelHakim99}.Comment: Review paper, 36 pages, 5 figure
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